My former employer (located in NY) sent me two W2s (I live in NJ). Do I need to enter both of them? They appear to be the same.

No, if the W-2 forms show identical amounts in every box of the forms then you should only enter one. Please view this TurboTax FAQ for more information about duplicate W-2s. 

Not if they're both identical you don't need to submit both forms.  But check them very closely.....there may be a slight difference in which case I think you should submit both but only put your income down once.